How should it challenge me? Well, I'm from a math background, so the natural choice is with arithmatic. A problem like 23*17 + 6 will keep me thinking for at least 20 seconds; if the alarm clock makes me solve five in a row, then it can be sure I'm awake. There's no way I can learn to do this in my sleep.
The design is powered by a PIC16 microcontroller, which manages the user interface and keeps time. It displays the current time and the arithmetic challenge via a cheap lcd from all electronics.
The design is free and open source; do whatever you want with it.
- A battery backup. As it stands, you must have enough will power to leave it plugged in.
- A radio? I suggest the Si4701 single-chip radio.